Complexity of Scalar Collapse in Anti-de Sitter Spacetime

We calculate the volume and action forms of holographic complexity for the gravitational collapse of scalar field matter in asymptotically anti-de Sitter spacetime, using numerical methods to reproduce the geometry responding to the oscillating field over multiple crossing times. Like the scalar field pulse, the volume complexity oscillates quasiperiodically before horizon formation. It also shows a scaling symmetry with the amplitude of the scalar field. The action complexity is also quasiperiodic with spikes of increasing amplitude.
Comment: 19pp; v2. added references, short discussion of Lloyd's bound for CV; v3. added discussion w/2 figs on complexity-momentum correspondence, minor clarifications; v4. typo corrections including to eqn (4.3), matches published version in content